Technical Mathematics

The mathematics department at Volunteer State Community College now offers a five semester hour course entitled, "Mathematics for Industrial Technology." In the past, the college has offered mathematics courses for general education, engineering, and business majors. The technical mathematics offering is a new direction.

In the fall of 1998 the college and Bosch Braking Systems joined with Nashville State Technical Institute to offer, for the first time, an 80 hour degree program for Bosch employees. Upon successful completion of the program these employees will receive an Associate's Degree in Industrial Technology. The timing of this program and of this Education Edge grant initiative provided an opportunity to develop an excellent technical mathematics course.

An important component of this degree program is the technical mathematics course. The authors built into this grant project the objective of developing an up-to-date mathematics course. The advantage here would be that the authors could develop this course in conjunction with people in business and industry who use mathematics every day.

After interviews and consultation with industry personnel, a new technical mathematics course emerged for the fall semester, 1998. Initially, this course will serve those in the Bosch Associate's Degree Program. However, it has the flexibility to serve the general population of students interested in a career in technology. It can also be used in other specialized programs that the college may design with other companies engaged in technological pursuits.

Appendix A provides a description of the syllabus for the new technical mathematics course.

Appendix A:
Mathematics 165
Mathematics for Industrial Technology

Description:

An integrated course in algebra, geometry, and trigonometry. Topics include but are not limited to: basic geometry, elements of trigonometry, solving systems of equations using determinants and matrices, vectors, oblique triangles, complex numbers, exponential and logarithmic functions, variation, conic sections, elementary statistics, elements of statistical process control, and metric measurement. Designed primarily for students in an Associates of Applied Science program in conjunction with a particular industry.

Prerequisites:

Two years of high school algebra and an acceptable score on the AAPP placement test, or DSM 086. The ability to use a graphing calculator is strongly recommended.

General Education Goals:

As a result of successfully completing this course, the student will have a sufficient mathematical foundation which will enable him or her to perform correct calculations and solve problems in an industrial setting.

Other Goals:

In addition to performing mathematical operations and becoming adept at problem solving, the student should be able to communicate his or her solution to a larger group in a clear and articulate manner.

Outcome Statements: Upon successful completion of this course, the student will have demonstrated the ability to perform each of the following operations.

Find the perimeter and area of the following two-dimensional figures: square, rectangle, circle, parallelogram, triangle, and trapezoid.

Measure angles in radians as well as degrees.

Use Simpson's Rule to find the area of irregularly shaped figures.

Find the surface area and volume of the following three-dimensional figures: cube, right circular cylinder, right prism, right circular cone, regular pyramid, sphere.

Solve contextual problems using all of the above mentioned concepts.

Find all of the following trigonometric ratios for any right triangle: sine, cosine, tangent, cosecant, secant, cotangent.

Given the appropriate information, be able to find any missing part of a right triangle in the context of an applied problem.

Find all of the trigonometric ratios of a general angle using the correct sign whether the angle is given in degrees or radians.

Convert any angle from radians to degrees and vice-versa.

Find the length of any circular arc.

Find the area of any circular sector.

Find the linear and angular velocity of any object moving in a circular motion.

Find the vector components of any object moving in any direction on a two-dimensional coordinate axis system.

Use the Law of Sines and the Law of Cosines to find any part of a general triangle.

Add, subtract, multiply, and divide complex numbers.

Find and simplify the product and quotient of any complex number in polar form.

Use DeMoivre's Theorem to find any power or root of a complex number in polar form.

Use the properties of exponents and the properties of logarithms to solve logarithmic and exponential equations.

Change the base of any logarithm to either base 10 or base e.

Interpret and create graphs of data on semi-log or log-log paper.

Find the any unknown part of a proportion.

Solve any applied problem where quantities vary directly, inversely, or jointly with each other.

Prove any trigonometric identity using the eight basic trigonometric identities, the sum and difference identities, the double-angle identities, and the half-angle identities.

Solve for any angle given a trigonometric function of that angle.

Simplify and solve a trigonometric equation to find an unknown angle.

Use the distance formula to find the distance between any two points on a coordinate axis system.

Find the slope of any line and apply it to various situations such as carpentry and road building.

Find, in any form, the equation of a straight line given the appropriate information about it.

Use the equation of a straight line to write a formula expressing one variable in terms of another.

Find all of the forms of the equation of a straight line i.e. point-slope, slope-intercept, and general.

Find the coordinates of the center and the radius of a circle given its equation either in standard of general form.

Given the coordinates of the center and the radius of a circle, write the equation for it in standard form.

Given a set of data, arrange it into frequency distributions by intervals, set up a frequency distribution table, and represent the data graphically by either a histogram or frequency polygon, or both.

Given a set of data, find the measures of central tendency i.e. mean, median, mode.

Given a set of data, find the standard deviation.

Use the Method of Least Squares to find the equation of the line that best fits a set of points obtained by collecting two sets of data.

Extend the Method of Least Squares to find the equation of the nonlinear curve which best fits a set of points obtained by collecting two sets of data.

Use the basic definitions of Statistical Process Control (SPC) to create and correctly interpret the following charts: X-R, np, p, c, and u.

Use dimensional analysis to convert units within the metric system as well as convert from metric to English and vice-versa.

Solve problems involving phenomena described by the equations in item 42 above.

Mathematics for Industrial Technology

Topical Outline

* Coverage may be modified to accommodate particular industry needs.

Units of Measurement; the Metric System

Introduction

Reductions and Conversions

Basic Geometry

Lines and Angles

Triangles

Quadrilaterals

Circles

Measurement of Irregular Areas

Solid Geometric Figures

The Trigonometric Functions

Angles

Defining the Trigonometric Functions

Values of the Trigonometric Functions

The Right Triangle

Application of Right Triangles

Determinants and Matrices

Determinants: Expansion by Minors

Some Properties of Determinants

Matrices: Definitions and Basic Operations

Multiplication of Matrices

Finding the Inverse of a Matrix

Matrices and Linear Equations

Trigonometric Functions of Any Angle

Signs of the Trigonometric Functions

Trigonometric Functions of Any Angle

Radians

Applications of the Use of Radian Measure

Vectors and Oblique Triangles

Introduction to Vectors

Components of Vectors

Vector Addition by Components

Applications of Vectors

Oblique Triangles, the Law of Sines

The Law of Cosines

Graphs of Trigonometric Functions

Graphs of y = a sin x and y = a cos x

Graphs of y = a sin bx and y = a cos bx

Graphs of y = a sin (bx + c) and y = a cos (bx + c)

Applications of Trigonometric Graphs

Complex Numbers

Basic Definitions

Basic Operations with Complex Numbers

Graphical Representation of Complex Numbers

Polar Form of a Complex Number

Exponential Form of a Complex Number

Products, Quotients, Powers, and Roots of Complex Numbers

An Application to Alternating Current (ac) Circuits

Variation

Ratio and Proportion

Variation

Additional Topics in Trigonometry

Fundamental Trigonometric Identities

Sine and Cosine of the Sum and Difference of Two Angles

Double-Angle Formulas

Half-Angle Formulas

Solving Trigonometric Equations

The Inverse Trigonometric Functions

Plane Analytic Geometry

Basic Definitions

The Straight Line

The Circle

Introduction to Statistics and Empirical Curve Fitting

Frequency Distributions

Measures of Central Tendency

Standard Deviation

Fitting a Straight Line to a Set of Points

Fitting Nonlinear Curves to Data

Statistical Process Control

X-R Charts

p charts

c charts

np charts

u charts

Problem Solving Tools

Assessment Techniques

Outcome statements will be assessed through in-class quizzes, tests, and problem solving. In addition, take-home assignments will be given. These assignments will involve application of course topics to various problem-solving situations. Homework problems will be assigned at each class meeting and discussed at each subsequent class meeting.

Evaluation and Attendance Policies

Evaluation: There will be 5 major tests (not including the final examination) during the semester. The major tests will be at least one hour in length. Each major test will count 100 points. There will also be several announced quizzes which will be 10-20 minutes in length. Each quiz will count 20 points.

Only the BEST FIVE quizzes will count toward the final grade in the course.

There will also be two special project assignments to be completed outside of class and turned in. These assignments will be worth 25 points each. Homework will be assigned at each class meeting.

It may be done in any format desired (i.e., loose leaf notebook, spiral notebook, folder..). It will be checked at the end of the semester for completeness and effort. Homework will count a maximum of 50 points.

There will be a final examination which will be selectively comprehensive. It will be worth 100 points. There is a total of 800 possible points to obtain.

Incomplete "I" Grade

A grade of "I" is designed only for severe emergencies such as car failure on the day of the final examination, death in the family, serious illness, or some life changing event. It will not be given in the situation where a student is merely behind in his or her work.

Inclement Weather Policy

If the College is closed due to extreme weather, this class will not meet and any events planned, i.e. test or quiz, will occur at the next class meeting. If the College is open, class will be held as usual.

Also any work due to be handed in on the date of a canceled class will be due at the next regularly scheduled meeting.

Attendance

Prompt and regular attendance is expected. Attendance will be recorded at every meeting. The College is required by federal law to keep attendance records for purposes of financial aid. See page 52 of the current catalog (1998-99).

Honesty Policy

Honorable and ethical behavior is expected regarding all course work. In any case where cheating is suspected, the student will be required to take an alternate test or do an alternate assignment.

In any case where there is absolute proof of cheating on any part of any course work, the student will receive an F in the course. Final decisions in these matters rest solely with the instructor.

Make-Up Work

Due to the frequency of quizzes, a missed quiz will not be made up and will be counted as a dropped grade. The first missed major test will be replaced by the student's grade on the final exam. If a student misses a second major test, he or she will be allowed to take a make-up test of significantly greater difficulty to replace that grade. This policy is in force regardless of the reasons why a student misses a test or a quiz.

Final Note

A mathematics class is driven by the question and answer format among all the participants, student and teacher alike. Therefore, everyone in the class is encouraged to ask a question or open discussion of a problem at any time. Some class time will be devoted to group work and group and individual presentations of problems and solutions. Everyone will be expected to be an active member of the class.

American Disabilities Act

In compliance with the American Disabilities Act, it is the student's responsibility to contact their instructors concerning any special accommodations required for completion of course requirements.

Volunteer State Community College is an equal opportunity Affirmative Action Educational Institution. No person shall be excluded from the participation in, be denied the benefit of, or be subjected to discrimination under any program or activity of the College because of race, color, national origin, age or handicap.